Most creative directors start out as a designer and work their way up. Depending on what type of Creative Director role you are after, you should focus your design career in that direction.
You mentioned brand management or advertising. The obvious career path for you would be to progress from an Art Director. (see more info in the link Ryan posted to the comments). If you take creative lead of some smaller projects (Art Director), eventually you will get put in charge of bigger ones. When you own bigger projects, you need people working with you, executing your vision (Creative Director). That is the difference between an Art Director and Creative Director, as far as Advertising/Marketing goes - it is just a bigger scope.
I've also seen some Creative Directors come from a non-design background, instead with marketing backgrounds - ideally you should have a bit of both. For Creative Director positions that are not graphically hands-on (usually in larger companies), you more importantly need to be a good leader and have an eye for quality.